IA175 Algorithms for Quantitative Verification

Faculty of Informatics
Autumn 2024
Extent and Intensity
2/1/1. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
prof. Dr. rer. nat. RNDr. Mgr. Bc. Jan Křetínský, Ph.D. (lecturer)
Guaranteed by
prof. Dr. rer. nat. RNDr. Mgr. Bc. Jan Křetínský, Ph.D.
Department of Computer Science – Faculty of Informatics
Supplier department: Department of Computer Science – Faculty of Informatics
Prerequisites
IB005
acquaintance with basic probability theory
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 39 fields of study the course is directly associated with, display
Course objectives
The course introduces
(1) several fundamental mathematical structures for modelling dynamic systems, where quantities such as probability, time, or cost are essential, and
(2) algorithms for their analysis, in particular their verification with respect to typical types of correctness requirements.
Besides, the course offers also a more practical experience with modelling and analysis tools.
Learning outcomes
The student can:
- model systems and their properties in appropriate mathematical formalisms
- can analyze the systems with respect to the properties using the discussed algorithms
- can choose appropriate algorithms for the analysis
- can design modifications of these algorithms and can rigorously argue about their correctness, complexity, and (dis)advantages
Syllabus
  • Motivation: verification, temporal logics, quantitative systems
  • Timed automata: modelling, semantics; reachability, region construction; zones, timed CTL
  • Markov chains: reachability, rewards, probabilistic LTL and CTL
  • Markov decision processes: modelling, semantics; reachability (linear programming, value iteration, strategy iteration; interval iteration, bounded real-time dynamic programming), rewards, probabilistic LTL and CTL; reinforcement learning and approximate dynamic programming; multi-objective optimization
  • Stochastic games: reachability (quadratic programing, value iteration, strategy iteration)
  • Systems with continuous time and space
Literature
    recommended literature
  • BAIER, Christel and Joost-Pieter KATOEN. Principles of model checking. Cambridge, Mass.: MIT Press, 2008, xvii, 975. ISBN 9780262026499. info
    not specified
  • MEYN, S. P. and R. L. TWEEDIE. Markov chains and stochastic stability. 2nd ed. Cambridge: Cambridge University Press, 2009, xxviii, 59. ISBN 9780521731829. info
  • Algorithmic game theory. Edited by Noam Nisan. Cambridge: Cambridge University Press, 2007, xxi, 754. ISBN 9780521872829. info
  • PUTERMAN, Martin L. Markov decision processes : discrete stochastic dynamic programming. Hoboken, N.J.: Wiley-Interscience, 2005, xvii, 649. ISBN 0471727822. info
  • FILAR, Jerzy A. and Koos VRIEZE. Competitive Markov decision processes : with 57 illustrations. New York: Springer, 1997, xii, 393. ISBN 0387948058. info
  • NORRIS, J. R. Markov chains. 1st pub. Cambridge: Cambridge University Press, 1997, xvi, 237. ISBN 9780521481816. info
  • PUTERMAN, Martin L. Markov decision processes : discrete stochastic dynamic programming. New York: Wiley, 1994, xvii, 649. ISBN 0471619779. info
Teaching methods
lectures, excercises, projects, homework, flipped classrooms
Assessment methods
exam + homework/project
Language of instruction
English
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2024/IA175